Change-point detection in time-series data by direct density-ratio estimation

Change-point detection is the problem of discovering time points at which properties of time-series data change. This covers a broad range of real-world problems and has been actively discussed in the community of statistics and data mining. In this paper, we present a novel non-parametric approach to detecting the change of probability distributions of sequence data. Our key idea is to estimate the ratio of probability densities, not the probability densities themselves. This formulation allows us to avoid non-parametric density estimation, which is known to be a difficult problem. We provide a change-point detection algorithm based on direct density-ratio estimation that can be computed very efficiently in an online manner. The usefulness of the proposed method is demonstrated through experiments using artificial and real datasets.